Geodesic
On the structure of multidimensional submanifolds with metric of revolution in Euclidean space
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 15 (2019) no. 2, pp. 192-202
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It is proved that a submanifold of low codimension with induced metric of revolution of sectional curvature of constant sign is a submanifold of revolution if the coordinate geodesic lines are the lines of curvature. 
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Alexander A. Borisenko. On the structure of multidimensional submanifolds with metric of revolution in Euclidean space. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 15 (2019) no. 2, pp. 192-202. http://geodesic.mathdoc.fr/item/JMAG_2019_15_2_a2/

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